Love Interests have always been Colour-Coded for Your Convenience. Traditionally, the hero's significant other would usually be a blonde, to contrast with the brunette Vamp or Femme Fatale. But today, the passive Damsel in Distress and Satellite Love Interest has been replaced by the sassy, bold, brash, sharp-tongued Action Girl — easily compatible with the "spunky Fiery Redhead" stereotype. In their relationship she will probably make him work to win her over for a long time or he won't realize that she's the one for him until the end. Naturally, it's quite common for the Veronica in a Betty and Veronica Love Triangle to be a redhead; the Betty will be a blonde.
Considering that less than 2% of the world's population has red hair (mainly among Celts, Scandinavians, and Ashkenazi Jews), there is a disproportionate number of red-haired characters out there, and an inordinate number of them are The Hero's winning Love Interest. (On top of that, they are also inordinately likely to have green eyes to go with it.) One possible source is Robert A. Heinlein's fondness for hypercapable red-haired heroines (he had a red-haired wife).
In European comics, the high proportion of redheads among the main protagonists has been explained by some authors by the simple fact that, since redheads are rare, they're easier to spot in the panels — especially true for crowd scenes.
Perhaps surprisingly to outsiders, given the (relatively) higher proportion of Irish redheads, this trope does not seem to exist in Ireland. Redheaded leads do appear, of course, but they are heavily outnumbered by the more common blondes and brunettes. This may be that, unlike almost everywhere else, red hair is not really seen as especially "exotic" in Ireland and Irish made media reflects this.
There isn't always a reason for this; if there is, sometimes, the red hair is symbolic of love and romantic desire, or the author just finds people that look like that appealing.
There are some cases where the redhead actually is The Hero. Please note that not every romance involving a red-head falls under this trope.
Oh, and this can apply to Evil Redhead, overlapping with Dating Catwoman.
Compare Everyone Loves Blondes, Red Is Heroic. Contrast Red-Headed Stepchild.